Input control in nonnegative matrix equations

In this paper we consider the nonnegative matrix system c_iA+u_iB=c_i+1 where the nonnegative matrix A is allowed to vary, within bounds. The cone control problem is to find a nonnegative matrix B such that if C_i is a nonnegative vector in a specified cone, then there is a nonnegative vector u_i such that c_i+1 is in that cone. We extend this problem to input control by finding a B such that the cone, generated by the rows of B, is as small as possible. Thus, the percent distribution of ∣u_iB∣ through the states of the sustem by u_iB is either constant or varies little.     

Metric marginal problems for set-valued or non-measurable variables

Summary In a separable metric space, if two Borel probability measures (laws) are nearby in a suitable metric, then there exist random variables with those laws which are nearby in probability. Specifically, by a well-known theorem of Strassen, the Prohorov distance between two laws is the infimum of Ky Fan distances of random variables with those laws. The present paper considers possible extensions of Strassen's theorem to two random elements one of which may be (compact) set-valued and/or non-measurable. There are positive results in finite-dimensional spaces, but with factors depending on the dimension. Examples show that such factors cannot entirely be avoided, so that the extension of Strassen's theorem to the present situation fails in infinite dimensions.This research was partially supported by a Guggenheim Fellowship, by National Science Foundation grant DMS 8505550 at MSRI-Berkeley, and other NSF grants     

An experiment to measure collisionless radial transport ofenergetic electrons confined by a dipole magnetic field

A new laboratory terrella has been constructed in order to study collisionless radial diffusion of particles trapped within a dipole magnetic field. Columbia's collisionless terrella experiment (CTX) aims to reproduce the process of wave-induced radial transport and does not try to simulate magnetospheric structure. The first experiment planned for CTX is the direct measurement of stochastic radial diffusion induced from wave-particle drift resonances. The motivation for the CTX experiment is described, and the procedures to be used to measure the intensity and spectrum of fluctuations generating chaos, the rate of radial transport, and the evolution of the density and pressure profiles are illustrated. Because of the success of similar experiments conducted earlier in a long thin magnetic mirror, these dipole experiments can be performed with a high degree of confidence. An example from these earlier experiments is presented     

The kinetics of the (5 × 20) → (1 × 1) structural transition for Au(100)

The kinetics of the anion-induced (5 × 20) → (1 × 1) surface structural transition of reconstructed Au(100) electrodes was studied in sulfate-containing solutions by current transients. It is shown that lifting of the reconstruction follows a nucleation-and-growth type behavior which can be described by the Avrami equation. Moreover, for high positive potentials, i.e., high anion coverages, the current-transient analysis reveals instantaneous nucleation, whereas for low transition overpotentials and long transition times a mechanism with constant transition rate prevails. Apparent activation energies, which depend strongly on the electrode potential, are derived from the temperature dependence of the Avrami plots.     

Phase diagram of multilayer magnetic structures

Multilayer ferromagnet-layered antiferromagnet (Fe/Cr) structures frustrated because of roughness of interlayer boundaries were studied by mathematical modeling methods. The phase diagram of a three-layer system (plotted as film thickness versus the degree of roughness of the interfaces) was obtained, and the order parameter distributions in each phase were determined. The character of phase transitions in this system was studied. The applicability range of the Slonczewski magnetic proximity model was determined.     

Fluorescence line narrowed spectra of Zn and metal-free cytochrome c

Fluorescence line narrowing (FLN) spectroscopy was used to study the role of the polypeptide chain in influencing the spectrum of Zn-substituted cytochrome c (Zn cyt c) and metal-free cyt c (porphyrin cyt c). For both derivatives the spectra show characteristics of relaxed fluorescence from an inhomogeneously broadened sample. Zero phonon lines and phonon wings can be clearly distinguished, and vibrational frequencies of the ground and excited states were identified. The inhomogeneous distribution width for porphyrin cyt c is slightly wider than that of Zn cyt c and a second population of molecules was apparent in the porphyrin cyt c. The phonon coupling was greater for Zn cyt c than for porphyrin cyt c, which may be due to the extra coupling to the polypeptide chain by metal ligation.This work has been done in partial fulfillment of the requirements for the Doctor of Philosophy degree.     

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%_b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study.